The \(\pi \) -tangle is a global negativity[1]}-based tripartite entanglement measure[2]}. While three-tangle cannot detect the tripartite entanglement
of the W-state class, \(\pi \) -tangle can detect it.
For a three-qubit state \(\rho \) 
the global negativities are given by
\({\cal N}^A = || \rho ^{T_A} || - 1, \hspace{28.45274pt}{\cal N}^B = || \rho ^{T_B} || - 1, \hspace{28.45274pt}{\cal N}^C = || \rho ^{T_C} || - 1,\) 
